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SPREAD WORLDS, PLENITUDE and MODAL REALISM: a PROBLEM for DAVID LEWIS by Charles R

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1 SPREAD WORLDS, PLENITUDE AND MODAL REALISM: A PROBLEM FOR DAVID LEWIS By Charles R. Pigden and Rebecca E. B. Entwisle 1. Introduction: Modal Realism and Meta-Philosophy David Lewis was famous (among other things) for the meta-philosophical claim that knock-down refutations are rare to non-existent in philosophy. You can argue that the costs of a theory exceed the intellectual benefits but it is difficult, if not impossible, to prove that it is false. When it comes to choosing between philosophical theories, it is generally a matter of ‘the price is right’, and when it comes to refuting a theory the best you can generally do is to drive up the costs whilst diminishing the benefits. There may come a time when the costs are so high and the benefits are so low that the theory can’t attract any takers, but this is usually due to a cumulative process of philosophical debate not to a sudden drop in net value brought about by a single decisive counterargument. When philosophers win, it’s nearly always a victory on points and almost never a knock-out. At the same time, Lewis subscribed to a philosophical thesis so outrageous as to cry out for knock-down refutation, namely that in order to make sense of modal truths, we must postulate an infinity of possible universes, all just as real as the one that we inhabit, but cut off from us in space and time. (This has the corollary that in order to make sense of causality we must postulate an infinity of items that have no causal connection to anything that happens in this universe.) Thus the temptation is to go for the double-whammy, the knock-down refutation of modal realism which is also a counterexample to the meta- philosophical claim. This was our aim when we first drafted this paper, but we can’t honestly claim the double victory that we originally hoped for. We may have given Lewis’s modal realism a drubbing but we don’t pretend to have decked it. Even if we have succeeded in driving up the costs of Lewis’s modal realism, it still retains enough benefits to attract some (rational) takers. Thus whatever the fate of Lewis’s philosophical thesis, the meta-philosophical claim remains intact. !We first wrote this article nearly twenty years ago when Lewis himself was very 2 much alive, but for one reason or another we never got around to publishing it. Rather than rewriting it to take account of the sad fact of his death we have decided to leave it in the present tense. We dedicate this paper not only to our friend and colleague, Colin Cheyne (who does not think we should believe in entities which cannot causally affect us), but to the memory of David Lewis, a great philosopher and a great teacher. 2. Modal Realism: Mad Dogs, Milksops and Primitives In his metaphysical summa of 1986, The Plurality of Worlds, (henceforward POW) David Lewis famously defends a doctrine he calls modal realism. The idea is that possible worlds are real, indeed really real. They are concrete entities just like our own world, but cut off from us in space and time. To every logically possible set-up there corresponds such a world. Lewis calls this the Principle of Plenitude. In fact, Lewis identifies his worlds with such set-ups - a move which makes it difficult to specify the Principle of Plenitude in a non-circular way (POW, pp. 86-92). Lycan (1988) calls this doctrine ‘mad dog’ modal realism’ ‘Rape-and-Loot modal realism’ and even ‘Nuclear Holocaust modal realism’, This is in contrast to moderate, milksop or, as Lewis describes it, ersatz modal realism. Ersatz realists believe in possible worlds all right. It is just that their possible worlds are less ontologically outrageous. Usually, they construct them out of actual entities of some kind: points, sets, sentences or what have you. This is ‘paradise on the cheap’, since we get all the theoretical advantages of possible worlds without the ontological drawbacks. !Lewis thinks he can do without modal primitives and that the milksop defenders of ersatz worlds cannot. This he holds to be the drawcard of an otherwise unpalatable theory. His possible worlds are admittedly implausible things (especially in such abundance) and the chief reason for believing in them, rather than in ersatz possibilia of some kind, is that they enable us to eliminate modal primitives. !Although sometimes denounced as a Meinongian, indeed a relentless Meinongian (Lycan, 1979), Lewis is, in fact, a rather heterodox Quinean. His aim is to explicate the modal concepts in terms of first order logic plus an ontology of possibilia. He retains a Quinean ideology, that is, the conviction that the resources of first-order logic, quantifiers, predicates, truth-functional connectives and the possible assistance of truth and 3 satisfaction, are adequate to describe reality.1 But unlike Quine (who prefers to believe there are no such things2) Lewis recognizes modal facts. To accommodate these facts within a Quinean ideology3, to explain the modalities in terms of quantification theory, Lewis has to invent more reality. The price of his ideological restraint is ontological inflation. He must posit an infinity of objects to quantify over. But it is important to realize that despite his ontological exuberance, what Lewis is putting forward is a reductive theory. It is just that the reductions are conceptual rather than ontological. The aim is to take the modality out of modality, to reduce modal to non-modal discourse even if the universe of discourse has to be inordinately expanded to do so. (It is for this reason that Plantinga (1987) denies Lewis his title to modal realism. For Plantinga, a modal realist must be a realist about modality and not just possibilia.) Moreover, in remaining true to the ideological constraints, Lewis has to ditch other aspects of the Quinean legacy. For Quine it is science that tells us What-There-Is. For Lewis that is true only of this world. Science tells us about that tiny portion of reality that is spatiotemporally related to us. As for the rest, a logically disciplined imagination is a better guide (POW, pp. 113-115). !The natural response to Lewis is a tu quoque. Milksop realists and plain modal sceptics have tried to pin Lewis down with modal primitives. They have tried to argue that he too implicitly relies on primitive notions of necessity and possibility. In which case his theory is no better than that of his milksop opponents, or indeed than the No- Theory Theory of Modality which simply assumes modal operators as primitives and leaves it at that. Indeed it is considerably worse off, since their ontologies are more believable. (See Lycan, 1988.) Our criticism is just such a riposte. !We shall argue that (on one reading) Lewis’s Principle of Plenitude licenses us to assume maverick possible worlds which spread through logical space gobbling up all the 1 Lewis’s ideological allegiance to Quine is most nakedly displayed in the opening paragraphs of his (1968) ‘Counterpart Theory and Quantified Modal Logic’. See also his POW pp. 1-20, and especially p. 4. However, in the nineties there was some degree of relaxation in Lewis’s ideological austerity. He came to accept the plural quantification theory of George Boolos. See Lewis (1991) Parts of Classes, especially pp. 62-71. But by adding the apparatus of plural quantification to his ideology, Lewis ceases to be a heterodox Quinean and becomes something close to an apostate. (Boolos is very explicitly an opponent of Quine. See his (1985) pp. 331-334.) We are inclined to think that this undermines the philosophical rationale for modal realism. After all, if we are allowed the ideological indulgence of plural quantification given the rather minimal ontological savings it brings in, why not allow us the further indulgence of modal primitives given that the ontological savings would be massive? 2 For an excellent survey of Quine’s views on modality and some sharp criticisms along the lines suggested see Haack (1979) ch. 10. 3 See Quine (1961) p. 131. 4 rest. Because they exclude alternatives, these worlds undermine Plenitude itself, and worse still, result in contradictions, since different spread worlds are incompatible with one another. Plainly the Principle of Plenitude must be amended to exclude these excluders. But, we maintain, this cannot be done without bringing in modal primitives. And once we admit modal primitives, bang goes the rationale for Lewis’s modal realism. We then consider various replies, the chief of which is due to Lewis himself. He insists that Plenitude does not license the spread worlds and hence that no amendment is needed. A fortiori no amendment is needed which requires him to make use of modal primitives. We answer that in that case his theory is disturbingly unspecific about which things are possible. Its intellectual value is therefore much diminished. Perhaps the price is no longer right. 3. The Principle of Plenitude: Some Preliminaries. What is the Principle of Plenitude? It appears in two versions, a naive version (absolutely every way a world could possibly be is the way that some world is), and an official version which relies on the Principle of Recombination. The official version is required since the naive version is trivialized once Lewis identifies worlds with ways worlds could possibly be. Both the official and the naive versions of Plenitude look like attempts to improve on another principle which we shall refer to as ur-Plenitude. It goes like this: to every consistent set of sentences there corresponds (at least) one possible world.
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